Anyone have issues with their ‘evidence’ when claiming their first benefit?

After 4 year of working part time at minimum wage I’ve finally had to bite the bullet and see if I’m able to claim any benefits, as I’m really struggling. To be honest, I’m really embarrassed by it.

I’ve been told I might qualify for Housing Benefit. I filled in the online form and have to go and take in all my evidence tomorrow at a Council Office. This includes my id, ‘original’ copy of my tenancy, wage slips etc.

But as I’m a joint tenant, I flat share with 2 other people through a private letting agent, I’ve been told I need to bring in evidence of them too! This includes id and their pay slips. Now I rung up the council and I explained they are not my family etc and we are not dependant on one another, but I was told I still need proof of who I live with. I went to my flat mates with this (which I didn’t want to due to embarrassment), one of them is totally fine with it but the other one (politely) refused. She said she doesn’t understand why they need her details and she is not happy with them having her details on file. Which I totally understand. I don’t get why they need their details either?!

Has anyone had any issue with this before? Will this mean they won’t process my claim?

Thanks.